1768:
1780:
1806:
1792:
168:), though simplified the computational processes, required long tables of numbers for its effective implementation. For timely use of these numbers they had to be memorised in toto and probably the system of constructing astronomical
1514:
1574:
1549:
1398:
886:
826:
1464:
1459:
911:
1201:
1544:
1529:
1368:
1569:
1837:
1752:
1589:
1519:
1418:
93:. These were routinely made use of for computations of native almanacs and for predicting the position of the Moon. The work ascribed to Vararuchi is also known as
1594:
1579:
1494:
1509:
1504:
1564:
1559:
1484:
1194:
675:
629:
810:
485:
232:
112:
1784:
1479:
1358:
1584:
1554:
1444:
137:
s. This is used in contrast to the modern mode computation of almanacs based on parameters derived from astronomical observations that are known as
1539:
1449:
801:
563:
Chandravakyas of vararuci: A practical guide for calculating the position of the sun and moon, namely, tithi and naksatra, on any day of the year
1746:
1489:
1187:
1257:
1474:
1454:
1413:
769:
589:
544:
1383:
1524:
408:, and has an average length of 27.554551 days (27 d 13 h 18 min 33.2 s). The apparent diameter of the Moon varies with this period. 9
1322:
906:
536:
1534:
1469:
1408:
1353:
1842:
1423:
1378:
1796:
1348:
1302:
581:
710:
Jones, Alexander (March 1983). "The development and transmission of 248-day schemes for lunar motion in ancient astronomy".
1086:
1428:
1403:
841:
794:
43:
of representation of numbers and so apparently appear like a list of words, or phrases or short sentences written in
452:
757:
1772:
1655:
1363:
690:
644:
1832:
1685:
1665:
1343:
500:
1499:
1388:
1297:
1287:
1096:
881:
836:
288:
108:
1625:
901:
787:
129:
were also popular in Tamil Nadu region of South India. There, the astrologers and astronomers used these
1726:
1125:
1262:
1055:
871:
1660:
719:
1307:
1247:
958:
891:
856:
761:
447:
1731:
1680:
1393:
1242:
916:
876:
831:
735:
442:
384:
is not fixed. In particular, the positions of the extreme points, the point of closest approach (
1690:
1615:
1277:
1222:
1081:
765:
607:
585:
540:
409:
405:
173:
40:
779:
31:) are a collection of numbers, arranged in the form of a list, related to the motion of the
1645:
1640:
1630:
931:
749:
727:
437:
268:
1705:
1695:
1670:
1635:
851:
750:
533:
Encyclopaedia of the history of science, technology, and medicine in non-western cultures
723:
1736:
1675:
1650:
1327:
1292:
1282:
1272:
1091:
1045:
1017:
1011:
1006:
926:
921:
1826:
1620:
1267:
1155:
1029:
993:
861:
739:
528:
1810:
1741:
1710:
1317:
1312:
1227:
1034:
1001:
941:
896:
404:, because it moved ahead during one revolution. This longer period is called the
1700:
1179:
1137:
1131:
333:
s). The authorship of this work is uncertain, but, is apocryphally assigned to
1610:
1232:
1167:
1076:
970:
350:
346:
1373:
1252:
1149:
1119:
1050:
866:
457:
413:
306:
161:
120:
78:
672:
For details on
Madhava's method of computation of Chandravakyas see :
133:
s to construct almanacs. These almanacs were popularly referred to as the
25:
1237:
1161:
1143:
1101:
936:
846:
334:
193:
189:
185:
177:
176:
provided the most convenient medium for constructing easily memorable
157:
52:
44:
731:
397:
385:
377:
272:
1515:
Indian
Institute of Science Education and Research, Thiruvananthapuram
412:
constitute a period of approximately 248 days. The differences in the
746:
For a discussion of the 248-day schemes in
Babylonian astronomy see:
416:
of the Moon on the successive days of a 248-day cycle constitute the
401:
389:
280:
197:
86:
317:. The next major work that makes use of the mnemonic system of the
708:
For a discussion on the history of the 248-day schemes see :
381:
276:
36:
1575:
Sree Chitra
Tirunal Institute for Medical Sciences and Technology
393:
373:
341:. It has been extensively commented upon by Sundararaja (c.1500
264:
244:
119:, together with a method for computing them, in his work titled
60:
32:
20:
1550:
National
Institute for Interdisciplinary Science and Technology
1183:
783:
342:
338:
216:
should have been around at the time of the institution of the
209:
201:
165:
82:
1399:
Kerala State
Council for Science, Technology and Environment
380:
rather than a circle. The orientation and the shape of this
231:
had been composed by astronomers and mathematicians of the
676:"Computation of the true moon by Madhava of Sangamagrama"
630:"Computation of the true moon by Madhava of Sangamagrama"
1465:
Aromatic and
Medicinal Plants Research Station, Odakkali
1460:
Amrita
Institute of Medical Sciences and Research Centre
392:), make a full circle in about nine years. It takes the
357:
for computing the almanacs. These almanacs are known as
247:'s motion contains 3031 numbers. There is a set of 2075
89:, is credited with the authorship of the collection of
85:), a legendary figure in the astronomical traditions of
200:
tradition has been determined as around fourth century
1545:
Mar
Athanasios College for Advanced Studies, Tiruvalla
1530:
Jubilee
Mission Medical College and Research Institute
1369:
Centre of Science and Technology for Rural Development
337:. The work is known to have been composed around 1300
1570:
Oriental Research Institute & Manuscripts Library
1719:
1603:
1437:
1336:
1215:
1110:
1064:
950:
817:
160:system of astronomical computations introduced by
1753:A History of the Kerala School of Hindu Astronomy
263:relating to the motion of the five planets Kuja (
1590:Tropical Botanical Garden and Research Institute
1520:Indian Institute of Space Science and Technology
1495:Centre for Marine Living Resources & Ecology
1419:Regional Agricultural Research Station, Pattambi
239:s contain a list of 248 numbers, another set of
1595:Vadakke Madham Brahmaswam Vedic Research Centre
1580:Srinivasa Ramanujan Institute of Basic Sciences
1195:
795:
8:
1510:Institute of Handloom and Textile Technology
1505:Crocodile Rehabilitation and Research Centre
1565:Naval Physical and Oceanographic Laboratory
1560:National Research Institute for Panchakarma
1485:Central Marine Fisheries Research Institute
1838:Kerala school of astronomy and mathematics
1202:
1188:
1180:
811:Kerala school of astronomy and mathematics
802:
788:
780:
718:(1). Berlin / Heidelberg: Springer: 1–36.
287:s encoding other mathematical tables like
188:are the earliest example of such a set of
172:s arose as an answer to this problem. The
113:Kerala school of astronomy and mathematics
1480:Central Institute of Fisheries Technology
1359:Centre for Mathematical Sciences (Kerala)
1585:St. Ephrem Ecumenical Research Institute
1555:National Institute of Speech and Hearing
1445:Agricultural Research Station, Anakkayam
578:Census of the Exact sciences in Sanskrit
493:Indian Journal of history of Mathematics
204:and the year of the promulgation of the
111:(c. 1350 – c. 1425), the founder of the
1540:Kerala School of Mathematics, Kozhikode
1450:Agricultural Research Station, Mannuthy
523:
521:
479:
477:
475:
473:
469:
396:longer to return to the same position,
388:) and the point of farthest excursion (
1747:Technology Business Incubator TBI-NITC
1490:Central Tuber Crops Research Institute
1475:Cashew Research Station, Madakkathara
1455:Agronomic Research Station, Chalakudy
1414:Rajiv Gandhi Centre for Biotechnology
1152:(Mahishamangalam Sankaran Namputhiri)
712:Archive for History of Exact Sciences
7:
1384:Kerala Science and Technology Museum
683:Indian Journal of History of Science
637:Indian Journal of History of Science
1791:
1525:Indian Institute of Spices Research
39:. These numbers are couched in the
301:The first known text to use these
115:, had set forth a revised set of
14:
887:Mazhamaṅgalaṃ Nārāyaṇan Naṃpūtiri
180:for the numbers in these tables.
1804:
1790:
1779:
1778:
1767:
1766:
1535:Kerala Forest Research Institute
1470:Banana Research Station, Kannara
1409:Liquid Propulsion Systems Centre
1354:Centre for Earth Science Studies
321:s which has come down to us is
1424:Rice Research Station, Moncombu
1379:Kerala Mathematical Association
752:The exact sciences in antiquity
1349:Centre for Development Studies
1303:Melpathur Narayana Bhattathiri
582:American Philosophical Society
486:"A Survey of Source Materials"
1:
1258:Jyā, koti-jyā and utkrama-jyā
1210:Scientific Research in Kerala
576:Pingree, David Erwin (1994).
329:, or computations, utilising
71:could thus be translated as
1429:Vikram Sarabhai Space Centre
1016:Laghuvivṛti (commentary on
689:(3): 231–253. Archived from
643:(3): 231–253. Archived from
261:Kujādi-pañcagraha-mahāvākyas
1404:Krishi Vigyan Kendra Kannur
1364:Centre for Rural Management
1138:Mahodayapuram (Kodungallur)
927:Śaṅkara Varma of Kaṭattanāṭ
283:). There are also lists of
67:means a sentence. The term
26:
1859:
1158:(Nilakantha Somayaji, etc)
1128:(Govinda Bhattathiri, etc)
1087:Madhava's correction terms
758:Courier Dover Publications
208:system is known to be 683
47:and hence the terminology
1762:
1656:Matthew Pothen Thekaekara
1146:(Madhava of Sangamagrama)
1122:(Azhvanchery Thamprakkal)
912:Śaṅkara of Mahiṣamaṅgalam
608:"Panchangam Calculations"
376:'s orbit approximates an
227:s, several other sets of
1686:T. A. Venkitasubramanian
1666:Pisharoth Rama Pisharoty
1344:C-DAC Thiruvananthapuram
1164:(Putumana Somayaji, etc)
902:Parameśvara of Vațaśśeri
748:Otto Neugebauer (1969).
674:K. Chandra Hari (2003).
628:K. Chandra Hari (2003).
565:. Adyar Library, Madras.
561:Raja, C. Kunhan (1946).
349:. The almanac makers of
35:in its orbit around the
1500:College of Horticulture
1389:Kerala Science Congress
1288:Madhava of Sangamagrama
882:Madhava of Sangamagrama
424:contains a list of 248
353:fully make use of this
109:Madhava of Sangamagrama
1843:Indian astronomy texts
1626:E. C. George Sudarshan
1111:Places associated with
1026:Mahābhāskarīya Bhāshya
499:: 1–20. Archived from
143:Thirukanitha Pañcāṅgas
1727:A Passage to Infinity
1113:members of the school
1023:Madhyamanayanaprakara
998:Jyotiśśāstra-saṃgraha
990:Jātaka-sāara-saṃgraha
987:Grahacāraṇinibandhana
957:Aryabhatiya-bhashya (
847:Dāmodara of Vațaśreņi
837:Azhvāñceri Taṃprākkaḷ
345:) of Trichinopopy of
315:Graha-cāra-nibandhana
1661:P. N. Vinayachandran
1298:Madhava's sine table
1162:Sivapuram (Thrissur)
1097:Madhava's sine table
606:Karanam, Ramakumar.
289:Madhava's sine table
1308:Nilakantha Somayaji
1248:Govinda Bhattathiri
959:Nīlakaņțha Sōmayāji
892:Nīlakaņțha Sōmayāji
857:Govinda Bhattathiri
724:1983AHES...29....1J
484:K.V. Sarma (1985).
365:Numbers encoded in
235:. While Vararuci's
223:Besides Vararuci's
1732:FORV Sagar Sampada
1681:Sainudeen Pattazhy
1394:Kerala Soil Museum
1243:Ganita-yukti-bhasa
877:Kochukrishnan Asan
820:and mathematicians
732:10.1007/bf00535977
506:on 11 January 2011
443:Indian mathematics
410:anomalistic months
1820:
1819:
1720:Assorted articles
1691:Thanu Padmanabhan
1616:C. V. Subramanian
1278:Katapayadi system
1223:Achyuta Pisharati
1177:
1176:
1140:(Sankaranarayana)
1082:Kaṭapayādi system
1077:Drigganita system
964:Candrachayaganita
917:Putumana Somayāji
771:978-0-486-22332-2
591:978-0-87169-213-9
546:978-0-7923-4066-9
406:anomalistic month
313:system, known as
309:'s manual on his
174:katapayadi system
41:katapayadi system
1850:
1811:India portal
1809:
1808:
1807:
1794:
1793:
1782:
1781:
1770:
1769:
1646:K. Radhakrishnan
1641:K. R. Ramanathan
1631:G. Madhavan Nair
1216:Pre 19th Century
1204:
1197:
1190:
1181:
1134:(Sankara Varman)
1039:Sidhhantadarpana
804:
797:
790:
781:
775:
755:
743:
705:
703:
701:
696:on 16 March 2012
695:
680:
660:
659:
657:
655:
650:on 16 March 2012
649:
634:
625:
619:
618:
616:
614:
603:
597:
595:
573:
567:
566:
558:
552:
550:
525:
516:
515:
513:
511:
505:
490:
481:
438:Indian astronomy
192:. The period of
81:(c. 4th century
29:
1858:
1857:
1853:
1852:
1851:
1849:
1848:
1847:
1833:Hindu astronomy
1823:
1822:
1821:
1816:
1805:
1803:
1758:
1715:
1706:Varghese Mathai
1696:Thomas Zacharia
1671:Pulickel Ajayan
1636:George Varghese
1599:
1433:
1332:
1323:Śaṅkaranārāyaṇa
1211:
1208:
1178:
1173:
1112:
1106:
1102:Parahita system
1065:Concepts/Topics
1060:
946:
922:Śankara Vāriyar
907:Śaṅkaranārāyaṇa
832:Acyuta Piṣāraṭi
827:(Complete list)
819:
813:
808:
772:
747:
709:
699:
697:
693:
678:
673:
669:
667:Further reading
664:
663:
653:
651:
647:
632:
627:
626:
622:
612:
610:
605:
604:
600:
592:
584:. p. 756.
575:
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519:
509:
507:
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488:
483:
482:
471:
466:
434:
370:
299:
154:
103:Pañcāṅgavākyāni
99:Vararucivākyāni
12:
11:
5:
1856:
1854:
1846:
1845:
1840:
1835:
1825:
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1818:
1817:
1815:
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1800:
1788:
1776:
1763:
1760:
1759:
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1756:
1749:
1744:
1739:
1737:Swatantra 2014
1734:
1729:
1723:
1721:
1717:
1716:
1714:
1713:
1708:
1703:
1698:
1693:
1688:
1683:
1678:
1676:R. S. Krishnan
1673:
1668:
1663:
1658:
1653:
1651:M. G. K. Menon
1648:
1643:
1638:
1633:
1628:
1623:
1618:
1613:
1607:
1605:
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1600:
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1577:
1572:
1567:
1562:
1557:
1552:
1547:
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1527:
1522:
1517:
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1457:
1452:
1447:
1441:
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1401:
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1338:
1334:
1333:
1331:
1330:
1328:Tantrasamgraha
1325:
1320:
1315:
1310:
1305:
1300:
1295:
1293:Madhava series
1290:
1285:
1283:Kriyakramakari
1280:
1275:
1273:Karanapaddhati
1270:
1265:
1260:
1255:
1250:
1245:
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1230:
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1219:
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1184:
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1135:
1129:
1123:
1116:
1114:
1108:
1107:
1105:
1104:
1099:
1094:
1092:Madhava series
1089:
1084:
1079:
1074:
1068:
1066:
1062:
1061:
1059:
1058:
1053:
1048:
1046:Tantrasamgraha
1043:
1040:
1037:
1032:
1027:
1024:
1021:
1018:Tantrasamgraha
1014:
1012:Kriyakramakari
1009:
1007:Karaṇapaddhati
1004:
999:
996:
991:
988:
985:
982:
979:
978:Gaṇitayuktayah
976:
973:
968:
965:
962:
954:
952:
948:
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939:
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598:
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568:
553:
545:
531:, ed. (1997).
529:Selin, Helaine
517:
468:
467:
465:
462:
461:
460:
455:
450:
445:
440:
433:
430:
428:or sentences.
420:. Each set of
369:
363:
359:Vākya-pañcāṅga
298:
296:Vākya-pañcāṅga
293:
257:Maṇḍala-vākyas
253:Samudra-vākyas
153:
147:
135:Vākya-pañcāṅga
95:Chandravākyāni
73:Moon-sentences
13:
10:
9:
6:
4:
3:
2:
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1624:
1622:
1621:Dileep George
1619:
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1350:
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1342:
1341:
1339:
1337:Organizations
1335:
1329:
1326:
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1321:
1319:
1316:
1314:
1311:
1309:
1306:
1304:
1301:
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1294:
1291:
1289:
1286:
1284:
1281:
1279:
1276:
1274:
1271:
1269:
1268:Jyotirmimamsa
1266:
1264:
1261:
1259:
1256:
1254:
1251:
1249:
1246:
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1072:Chandravakyas
1070:
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966:
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932:Udayadivākara
930:
928:
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897:Nīlakaṇṭha II
895:
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451:
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418:Chandravākyas
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367:Chandravākyās
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303:Chandravākyas
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214:Chandravākyās
212:, Vararuci's
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139:Dṛk Pañcāṅgas
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42:
38:
34:
30:
28:
22:
18:
17:Chandravākyas
1802:
1795:
1783:
1771:
1751:
1742:Techno-lodge
1711:Vinod Scaria
1438:Institutions
1318:Sadratnamala
1313:Parameshvara
1228:Candravakyas
1071:
1042:Spuṭanirṇaya
1035:Sadratnamālā
1002:Kanakkusāraṃ
942:Vidyamadhava
776:(Chapter II)
751:
715:
711:
698:. Retrieved
691:the original
686:
682:
652:. Retrieved
645:the original
640:
636:
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601:
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556:
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501:the original
496:
492:
425:
421:
417:
371:
366:
358:
355:Vākya-karaṇa
354:
330:
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323:Vākya-karaṇa
322:
318:
314:
310:
302:
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295:
284:
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260:
256:
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243:relating to
240:
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184:ascribed to
181:
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1797:WikiProject
1701:Vainu Bappu
1263:Jyeṣṭhadeva
1170:(Haridatta)
1132:Kadathanadu
872:Jyeṣṭhadeva
818:Astronomers
760:. pp.
448:Vākyakaraṇa
275:), Bhrigu (
1827:Categories
1611:Ajit Varki
1604:Scientists
1233:Citrabhanu
1168:Tirunavaya
1056:Yuktibhāṣā
1030:Pañcabodha
971:Drigganita
967:Dasādhyāyi
937:Vararuci I
842:Citrabhānu
464:References
414:longitudes
351:Tamil Nadu
347:Tamil Nadu
267:), Budha (
1773:Templates
1374:Cyberpark
1253:Haridatta
1150:Peruvanam
1126:Alathiyur
1120:Athavanad
1051:Venvaroha
975:Dṛkkaraṇa
951:Treatises
867:Haridatta
852:Devācārya
740:121595932
458:Vararuchi
307:Haridatta
271:), Guru (
251:s called
190:mnemonics
178:mnemonics
164:(ca. 683
162:Haridatta
152:tradition
121:Venvaroha
79:Vararuchi
1785:Category
1238:Damodara
1144:Kudallur
984:Golasara
981:Golavada
537:Springer
432:See also
335:Vararuci
311:Parahita
220:system.
218:Parahita
206:Parahita
194:Vararuci
186:Vararuci
158:Parahita
53:Sanskrit
45:Sanskrit
720:Bibcode
596:(p.558)
551:(p.522)
398:perigee
386:perigee
378:ellipse
273:Jupiter
269:Mercury
59:is the
57:Chandra
768:
738:
588:
543:
426:Vākyās
402:apogee
390:apogee
327:karaṇa
281:Saturn
241:Vākyas
229:Vākyas
198:Kerala
87:Kerala
736:S2CID
700:6 May
694:(PDF)
679:(PDF)
654:6 May
648:(PDF)
633:(PDF)
613:5 May
510:3 May
504:(PDF)
489:(PDF)
382:orbit
331:Vākya
319:Vākya
305:s is
285:Vākya
277:Venus
249:Vākya
237:Vākya
225:Vākya
170:Vākya
150:Vākya
141:( or
131:vākyā
101:, or
97:, or
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63:and
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37:Earth
766:ISBN
702:2010
656:2010
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586:ISBN
541:ISBN
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394:Moon
374:Moon
372:The
265:Mars
245:Moon
156:The
61:Moon
33:Moon
21:IAST
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400:or
361:s.
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